Before police can enter a home in pursuit of a fleeing suspect, they need to be able to articulate the crime the fleeing suspect is suspected of committing. If the crime is a felony, the hot pursuit exception will generally justify the warrantless entry
In the proximity of a potential on-going felony, they can enter. However, they are limited to the immediate circumstances. Example, they break in to a home while in active pursuit and dont find the suspect but find an illegal poker game. Cannot use the search to justify arresting the game players or seizing the cash.
Do the police have the right to enter the home without a warrant and search the home?
They can search the house for the suspect, but they cant search for a bag of weed under the couch.
Hot pursuit is a recognized exception to the warrant requirement of the 4th Amendment. See for example United States v. Santana, 427 U.S. 38 (1976) among many other cases.
Yes, they can enter a house if they are in hot pursuit of a felon. Leaving the scene of an accident is a felony in most states.
However, he cannot use that to discover information about another crime.